Final answer:
To find the equation of line s, we need to determine its slope and y-intercept. Since line s is perpendicular to line r, the slope of line s will be the negative reciprocal of the slope of line r. The equation of line s is y = (1/3)x - 7.
Step-by-step explanation:
The equation of line r is 3x + y = 4. To find the equation of line s, we need to determine its slope and y-intercept. Since line s is perpendicular to line r, the slope of line s will be the negative reciprocal of the slope of line r.
Let's find the slope of line r. Rearranging the equation 3x + y = 4 in the slope-intercept form y = mx + b, where m is the slope, we get y = -3x + 4. So, the slope of line r is -3.
The slope of line s will be the negative reciprocal of -3, which is 1/3. Since line s includes the point (6, -5), we can use the slope-intercept form y = mx + b to represent the equation of line s.
Substituting the slope 1/3 and the coordinates (6, -5) into the equation, we have:
-5 = (1/3)(6) + b
Rearranging the equation, we can find the value of b:
b = -5 - 2 = -7
Therefore, the equation of line s is y = (1/3)x - 7.